《Mathematical Methods in Physics and Engineering》求取 ⇩

作者 John W.Dettman 编者
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Mathematical Methods in Physics and Engineering PDF电子版封面 John W.Dettman

CHAPTER 1．Algebraic Preliminaries1

1．1Linear Equations．Summation Convention1

1．2 Matrices5

1．3 Determinants8

1．4 Systems of Linear Algebraic Equations．Ranks of a Matrix15

1．5 Vector Spaces18

1．6 Scalar Product24

1．7 Orthonormal Basis．Linear Transformations30

1．8 Infinite-dimensional Vector Spaces．Function Space35

1．9 Fourier Series44

1．10 Quadratic Forms．Hermitian Forms53

1．11 Systems of Ordinary Differential Equations．Vibrations Problems62

CHAPTER 2．Calculus of Variations68

2．1Maxima and Minima of Functions．Lagrange Multipliers68

2．2 Maxima and Minima of Functionals．Euler＇s Equation76

2．3 Hamilton＇s Principle．Lagrange＇s Equations89

2．4 Theory of Small Vibrations96

2．5 The Vibrating String99

2．6 Boundary-value Problems of Mathematical Physics108

2．7 Eigenvalues and Eigenfunctions117

2．8 Eigenfunction Expansions125

2．9 Upper and Lower Bounds for Eigenvalues129

CHAPTER 3．Boundary-value Problems．Separation of Variables137

3．1Orthogonal Coordinate Systems．Separation of Variables137

3．2 Sturm-Liouville Problems．Fourier Series149

3．3 Series Solutions of Ordinary Differential Equations162

3．4 Series Solutions of Boundary-value Problems176

CHAPTER 4．Boundary-value Problems．Green＇s Functions184

4．1Nonhomogeneous Boundary-value Problems184

4．2 One-dimensional Green＇s Functions190

4．3 Green＇s Functions in Higher Dimensions201

4．4 Problems in Unbounded Regions207

4．5 A Problem in Diffraction Theory219

CHAPTER 5．Integral Equations．226

5．1Integral Equations Formulation of Boundary-value Problems226

5．2 Hilbert-Schmidt Theory230

5．3 Fredholm Theory246

5．4 Integral Equations of the First Kind260

CHAPTER 6．Integral Transform Methods266

6．1Fourier Transforms266

6．2 Applications of Fourier Transforms．Ordinary Differential Equations277

6．3 Applications of Fourier Transforms．Partial Differential Equations283

6．4 Applications of Fourier Transforms．Integral Equations291

6．5 Laplace Transforms．Applications297

6．6 Other Transform Techniques310

Index319

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